Delayed Line Paths Animation
When you create a Follow Path constraint, it automatically gives the curve an Animation Generator modifier. If you want to control this animation manually you need to delete this generator in the Graph Editor > properties panel (N). Then you'll be able to give some keyframes in the Properties panel > Data > Path animation > Evaluation Time value of your curve.

You can test: when you change the Evaluation Time value, it moves your object along the curve. So put your cursor where you want in the timeline, move the object where you want along the curve with this Evaluation Time value, then put your cursor over the Evaluation Time and press i, then create a second keyframe wherever you want on the timeline, and the object will interpolate.